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Description:
We investigate the limit passage for a system of slow and fast chemical reactions of mass-action type, where the rates of fast reactions tend to infinity. We give an elementary proof of convergence to a reduced dynamical system on the manifold of fast reaction equilibria. Then we study the entropic gradient structure of these systems and prove an E-convergence result via $\Gamma$-convergence of the primary and dual dissipation potentials, which shows that this structure carries over to the fast reaction limit in a thermodynamically consistent way. We recover the limit dynamics as a gradient flow of the entropy with respect to a pseudo-metric.